# How is the image in a mirror created? Are there infinitely many light rays?

How is the image in a mirror created? Are there infinitely many light rays?

My motivation for the question is from image processing. We work with images as discrete 2D functions, as matrices. Spatial sampling is done, and also quantization. Then I thought, well that is far from perfect, I wonder how does God create images? And then I thought of a real example, well, the mirror! The 3D world is projected on a 2D plane, the mirror. So how many rays arrive on the mirror? Infinitely many? Does God do spatial sampling or is the image in the mirror continuous?

• By "God" do you happen to happen to mean "image sensors" or "retina"?
– user12029
Apr 2 '14 at 0:57

The approximate number of photons which strike a mirror and enter your eye over the period of a couple seconds is a massive quantity (in Mathematica):

<< PhysicalConstants
Convert[(1 Milli Joule 600 Nano Meter)/(PlanckConstant SpeedOfLight), 1]
`

Output:

3.02047*10^15

Since this is in the quadrillions, for all practical intents and purposes, the number of individual rays that the photons striking a mirror in your living room/bathroom and enter your eye is enough to consider it a continuum of rays forming an image.

However, despite this large number, our bodies are imperfect, and there are limits on the resolution imposed by the optical properties of our body. In image processing language, there is a point spread function associated with our eye's ability to resolve objects in our field of view; the image we see is the actual image convolved with the point spread function of our vision.

So even though there are a gigantic number of rays being traced, we're still limited by our body's ability to spatially resolve them.

Nothing in the universe is continuous. Matter and light are made up of particles, and physicists have strong reason to believe that even space is quantised.

As for the mirror, photons travel from the lightsource to the object. There they are either absorbed or reflected, depending on their wavelength and the properties of the object at the point of interaction. The reflected photons leave the object, and some of them will hit the mirror, which reflects most of them (and absorbs the rest).

The number of photons hitting us is not infinite (nothing is, except perhaps the universe/multiverse, but the answer to that is not in yet), but we are struck by a huge number of them. The sun emits enough photons so that approximately $3.6*10^{21}$ photons strike each square metre of the earth every second.

If the object reflects 50% of the photons and the mirror 99%, that still leaves $1.78*10^{21}$ photons per square meter per second - close enough to infinity for me.